Publication details
Homogeneous Einstein metrics on generalized flag manifolds Sp(n)/(U(p)×U(q)×Sp(n−p−q))
| Authors | |
|---|---|
| Year of publication | 2011 |
| Type | Article in Proceedings |
| Conference | Recent progress in differential geometry and its related fields : Proceedings of the 2nd International Colloquium on Differential Geometry and its Related Fields |
| Citation | |
| Web | https://www.worldscientific.com/doi/suppl/10.1142/8187/suppl_file/8187_chap01.pdf |
| Doi | http://dx.doi.org/10.1142/9789814355476_0001 |
| Keywords | Homogeneous Einstein metric; Generalized flag manifold; Gröbner basis |
| Description | We construct the Einstein equation for an invariant Riemannian metric on generalized flag manifolds Sp(n)/(U(p) × U(q) × Sp(n - p - q)). By computing a Gröbner basis for a system of polynomials on six variables, we prove that the generalized flag manifolds Sp(3)/(U(1) × U(1) × Sp(1)), Sp(4)/(U(1) × U(1) × Sp(2)) and Sp(4)/(U(2) × U(1) × Sp(1)) admit exactly three, six and two non-Kähler invariant Einstein metrics up to isometry, respectively. |